primality

Alexa's Conjecture on Primality ★★

Author(s): Alexa

Definition Let $r_i$ be a non negative integer such that :

$(2i+1)^{p-1} \equiv r_i \pmod p ~~\text{ and } ~ r_i < p , ~\text{where}~ i , p \in \mathbb{N}$

Conjecture Natural number $p$ ; $(p \geq 8)$ is a prime iff

$\displaystyle \sum_{i=1}^{\left \lfloor \frac{\sqrt[3]p}{2} \right \rfloor} r_i = \left \lfloor \frac{\sqrt[3]p}{2} \right \rfloor$

Keywords: primality

Posted by princeps
updated April 2nd, 2012

Conjecture $p$ is a prime iff $~\displaystyle \sum_{i=1}^{p-1} i^{p-1} \equiv -1 \pmod p$

Keywords: primality

Posted by princeps
updated March 27th, 2012

Author(s): McEachen

Conjecture Every odd prime number must either be adjacent to, or a prime distance away from a primorial or primorial product.

Posted by billymac00
updated July 7th, 2012